Querying, storing, and using data from 2 separate custom post types

For custom field queries you can’t use an array for multiple keys, unfortunately. What you want is something like this:

$args = array(
    'post_type' => array('gym_location', 'gym_term'),
    'orderby' => 'title',
    'order' => 'DESC',
    'meta_query' => array(
        array(
            'key' => 'term_active',
            'value' => '1',
            'compare' => '=='
        ),
        array(
            'key' => 'location_active',
            'value' => '1',
            'compare' => '=='
        ),
        'relation' => 'OR',
    )
);

See https://codex.wordpress.org/Class_Reference/WP_Query#Custom_Field_Parameters